Consider the bond market to be in equilibrium according to our complete theory o
ID: 2771884 • Letter: C
Question
Consider the bond market to be in equilibrium according to our complete theory of the term structure of interest rates. The current interest rate on one-year bonds is 5 percent, and you believe, as does everyone in the market, that in one year the interest rate on one-year bonds will be 6 percent and in two years the interest rate on one-year bonds will be 6.5 percent. Assume that there is no term premium on a one-year bond. Suppose the term premium equals 0.5 percent ´ the number of years to maturity, for two-year bonds and three-year bonds. The interest rate today on the two-year bond is ____ and the interest rate today on a three-year bond is ____.
Select one:
a. 5.5 percent; 5.8 percent
b. 6.0 percent; 6.3 percent
c. 6.2 percent; 6.8 percent
d. 6.5 percent; 7.3 percent
Explanation / Answer
To calculate the interest rate as per theory of the term structure of interest rates, we need to find the average of the short term interest rates expected in the near future. The formula for calculating the same can be derived as follows:
Bond Interest Rate (for 2 Year Bond) = (Current Interest Rate + Interest Rate Year 1)/2
Bond Interest Rate (for 3 Year Bond) = (Current Interest Rate + Interest Rate Year 1 + Interest Rate in Year 3)/3
Bond Interest Rate With Premium = Bond Interest Rate (for respective year)+ .50*(t) where is years to maturity
_____________
Using the information provided in the question, we get,
Bond Interest Rate (for 2 Year Bond) = (5% + 6%)/2 = 5.5%
Bond Interest Rate (for 3 Year Bond) = (5% + 6% + 6.5%)/3 = 5.8%
_____________
Bond Interest Rate (for 2 Year Bond) with Premium = 5.5% + .50*2 = 6.5%
Bond Interest Rate (for 3 Year Bond) with Premium = 5.8% + .50*3 = 7.3%
Answer is 6.5 percent; 7.3 percent (which is Option D)